Method for controlling surface errors of sample in homogeneity measurement of infrared optical materials

ABSTRACT

Disclosed is a method for controlling surface errors of a sample in a homogeneity measurement of infrared optical materials. In this invention, a calculation relationship among the surface errors, measurement principles and precision requirements is established. The wavefront distortion caused by the surface errors of the sample measured in infrared wavebands is converted to the surface errors of the sample which is processed and inspected under the visible light. Through establishing related algorithms and formulas for numerical calculations, a numerical table for controlling the surface errors of the sample is created to ensure the precision of the homogeneity measurement for the infrared optical material under short, middle and long wavebands. A case table for controlling the surface errors of the sample is also provided to ensure the precision of the homogeneity measurement for the specific infrared optical materials under short, middle and long wavebands.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of International Patent ApplicationNo. PCT/CN2019/109386, with a filling date of Sep. 27, 2019, designatingthe United States, now pending, and further claims the benefit ofpriority from Chinese Patent Application No. 201811219047.1, with afilling date of Oct. 19, 2018. The content of the aforementionedapplications, including any intervening amendments thereto, isincorporated herein by reference in its entirety.

TECHNICAL FIELD

The present application relates to homogeneity measurements for infraredoptical materials, and more particularly to a method for controlling thesurface errors of a sample in homogeneity measurements of infraredoptical materials.

BACKGROUND OF THE INVENTION

The homogeneity measurement of infrared optical materials is ahigh-precision measurement, in which a refractive index homogeneity ofthe infrared optical material is measured. The measurement method is aninterferometry in which a wavefront distortion of plane waves of testbeams caused by inhomogeneity of the infrared optical material isobtained through an interferometer. The measurement precision is usuallyrequired up to 1×10⁻⁴-1×10⁻⁵ due to different measurement precisionrequirements. In order to ensure the high precision of the refractiveindex homogeneity measurement, a general approach is to improve theprecisions of measurement equipment and measurement methods. In fact,the high-precision measurement cannot be achieved merely throughimproving the precisions of measurement equipment and measurementmethods, even though the ambient temperature influence on themeasurement precision in the measurement room is also required to beevaluated and controlled. In addition, the surface errors or flatnesserrors of the sample also greatly affect the measurement precision. Thesurface errors of the sample can cause wavefront distortion of the beamthat transmits through the sample, which can be observed through aninterferometer. However, the phenomenon of the wavefront distortioncaused by the surface errors of the sample is the same as the that ofthe wavefront distortion caused by the refractive index inhomogeneity ofthe infrared optical material. Therefore, it is impossible todistinguish the wavefront distortion caused by the surface errors of thesample from the wavefront distortion caused by the refractive indexinhomogeneity of infrared optical materials. Thus, in order to ensurethe precision of the homogeneity measurement of the infrared opticalmaterial, it is required to find a method to calculate the impact ofsurface errors of the sample on refractive index homogeneity measurementof the materials and calculate a reference value for controlling thesurface errors of the sample, so as to realize an accurate quantitativecontrol for the surface processing of samples and guarantee that resultsof the homogeneity measurement for infrared optical materials are onlyinfluenced by the inhomogeneity of the optical materials, thereby makingmeasurement results reflect actual situations of the materialinhomogeneity.

In the prior art, there is no algorithm to quantitatively calculate thesurface errors of the sample in the homogeneity measurement of infraredoptical materials. Though it is known that the surface errors of thesample adversely affect the measurement precision, there is no algorithmto analyze how much the surface errors affect the measurement results.Therefore, the sample optical surface is merely required to be processedas well as possible, causing that the optical surface of the sample isprone to being insufficiently or excessively processed. When the opticalsurface of the sample is insufficiently processed, the homogeneitymeasurement of the infrared optical materials is carried out with thesurface errors of the sample that is significantly higher than thesurface errors required by the measurement precision, resulting in theunbelievable and useless results of the homogeneity measurement of theinfrared optical materials. When the optical surface of the sample isexcessively processed, high cost should be paid to process the sample,resulting in waste of money and time.

SUMMARY OF THE INVENTION

This invention aims to provide a method for controlling surface errorsof a sample in homogeneity measurement of infrared optical materials, bywhich the surface errors of the sample are accurately controlled toensure an intended precision of the homogeneity measurement of theinfrared optical materials.

The technical solutions of the invention are described as follows.

The invention provides a method for controlling surface errors of asample in homogeneity measurement of infrared optical materials,comprising:

1) setting the surface error of the sample as S_(im), a nominalrefractive index of the sample as n₀, the number of times with which aninfrared radiation flux transmits through the sample as N and awavefront distortion of reference beam waves caused by the surfaceerrors of the sample as ΔW_(S); and calculating ΔW_(S) according toequation (1):

ΔW _(S)=2N(n ₀−1)S _(im)  (1);

2) establishing a relationship between the wavefront distortion ΔW_(S)and a wave error ΔW_(p) of permissible precision requirements of aninterferometer for refractive index homogeneity measurements:

ΔW _(S) ≤kΔW _(P)  (2);

wherein k is the precision control factor;

plugging the equation (1) into the inequation (2) to obtain inequation(3):

$\begin{matrix}{{S_{im} \leq {k\frac{\Delta W_{p}}{2{N\left( {n_{0} - 1} \right)}}}};} & (3)\end{matrix}$

3) determining the number N according to measurement principle of theinterferometer;

4) obtaining the wavefront error ΔW_(p) of the permissible precisionrequirements of an interferometer according to permissible precision ofthe interferometer:

calculating the wave error ΔW_(p) according to equation (4):

$\begin{matrix}{{{\Delta W_{p}} = \frac{\lambda_{i}}{5}};} & (4)\end{matrix}$

wherein λ_(i) is the infrared wavelength for measurement;

plugging the equation (4) into the inequation (3) to obtain inequation(5):

$\begin{matrix}{{S_{im} \leq {k\frac{\lambda_{i}}{10{N\left( {n_{0} - 1} \right)}}}};} & (5)\end{matrix}$

5) setting a visible wavelength for inspecting an infrared opticalsample as λ_(v), and setting a ratio of the infrared wavelength λ_(i) tothe visible wavelength λ_(v) as R;

wherein R is expressed as equation (6):

$\begin{matrix}{{R = \frac{\lambda_{i}}{\lambda_{v}}};} & (6)\end{matrix}$

(6) plugging the equation (6) into the inequation (5) to obtaininequation (7), so that the surface errors of the sample are measuredwith the visible wavelength, wherein the inequation (7) is expressed as:

$\begin{matrix}{{S_{im} \leq {k\frac{R\lambda_{v}}{10{N\left( {n_{0} - 1} \right)}}}};} & (7)\end{matrix}$

7) since the visible wavelength λ_(v) is 0.6328 and infrared wavebandsare classified into a short infrared waveband with a mean wavelengthλ_(s) of 2 μm, a middle infrared waveband with a mean wavelength λ_(m)of 4 μm and a long infrared waveband with a mean wavelength λ₁ of 10 μm,dividing λ_(s) by λ_(v) to obtain a ratio R_(s) of approximately 3.16:1;dividing λ_(m) by λ_(v) to obtain a ratio R_(m) of approximately 6.32:1;and dividing λ₁ by λ_(v) to obtain a ratio R₁ of approximately 15.8:1;

8) plugging the ratios R_(s), R_(m) and R₁ obtained in step 7) into theinequation (7) to establish a numerical table for controlling of thesurface errors of the sample corresponding to precision requirements ofthe homogeneity measurements for infrared optical materials, therebyestablishing a relationship between control values of the surface errorsof the sample and various precision requirements for the measurementapplications of various infrared wavebands and interferometers whichvary in principles; and

(9) controlling the surface errors of the sample in the homogeneitymeasurements of infrared optical materials based on the precisionrequirements of the homogeneity measurements of the infrared opticalmaterials and the surface errors shown in the numerical table.

In an embodiment, k is 1, ½ or ⅓, and the smaller a value of k, thesmaller an influence of the surface errors of the sample on themeasurement precision.

In an embodiment, in step (3), the infrared radiation flux transmitsthrough the sample twice (N=2) when a Fizeau interferometer is used tomeasure the refractive index homogeneity; the infrared radiation fluxtransmits through the sample twice (N=2) when a Twyman-Greeninterferometer is used to measure refractive index homogeneity; and theinfrared radiation flux transmits through the sample once (N=1) when aMach-Zehnder interferometer. is used to measure the refractive indexhomogeneity.

In an embodiment, the numerical table established in step (8) is shownin Table 1:

TABLE 1 Numerical table for controlling the surface errors of the samplecorresponding to the precision requirements of the homogeneitymeasurements for infrared optical materials Number of times the infraredradiation flux Permissible surface errors in visible waveband transmitsthrough the Short infrared Middle infrared Long infrared sample wavebandwaveband waveband N = 1 $k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.58\lambda_{v}}{n_{0} - 1}$ N = 2 (without consideration ofsurface error mutual $k\frac{0.158\lambda_{v}}{n_{0} - 1}$$k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.79\lambda_{v}}{n_{0} - 1}$ offsetting) N = 2 (with surfaceerror mutual offsetting) $k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.264\lambda_{v}}{n_{0} - 1}$$k\frac{3.16\lambda_{v}}{n_{0} - 1}$

In an embodiment, the surface errors of the sample for the homogeneitymeasurements are equal to or less than the values shown in Table 1.

In an embodiment, in Table 1, there are two measurement principles whenN=2; one measurement principle is that the sample shape for measuring isa plane parallel plate sample, and the other measurement principle isthat a sample shape for measuring is a wedge-shaped sample; andrequirements of the surface errors of the wedge-shaped sample arelowered, since the surface errors of the sample are mutually subtractedby a measurement principle of the wedge-shaped sample.

In an embodiment, before the step 9), the method further comprises:

plugging the precision control factor k of 1 and a nominal refractiveindex n₀ of an infrared chalcogenide optical material of 2.6 to obtain acase table 2:

TABLE 2 Case table for controlling the surface errors of the samplecorresponding to the precision requirements of the homogeneitymeasurements for infrared optical materials Number of times the infraredradiation flux Permissible surface errors in visible waveband transmitsthrough the Short infrared Middle infrared Long infrared sample wavebandwaveband waveband N = 1 λ_(v)/5 2λ_(v)/5 λ_(v) N = 2 λ_(v)/10 λ_(v)/5λ_(v)/2 (without consideration of surface error mutual offsetting) N = 22λ_(v)/5 4λ_(v)/5 2λ_(v) (with surface error mutual offsetting)

In an embodiment, in step (9), the surface errors of the sample in thehomogeneity measurements of the infrared chalcogenide optical materialsand other infrared optical materials with refractive indexes same ornearly same to refractive indexes of the infrared chalcogenide opticalmaterials are controlled based on the precision requirements of thehomogeneity measurements of infrared optical materials and the surfaceerrors of the sample shown in Table 2. Most of the infrared opticalmaterials in the application have a refractive index of 2.6 or nearly2.6.

The beneficial effects of the invention are described as follows.

In this invention, a calculation relationship among the surface errors,measurement principles and precision requirements is established. Thewavefront distortion caused by the surface errors of the sample measuredin infrared wavebands is converted to the surface errors of the samplewhich is processed and inspected under the visible light. Throughestablishing related algorithms and formulas for numerical calculations,a numerical table for controlling the surface errors of the sample iscreated to ensure the precision of the homogeneity measurement forinfrared optical materials under short, middle and long wavebands. Acase table for controlling the surface errors of the sample is alsoprovided to ensure the precision of the homogeneity measurement for thespecific infrared optical materials under short, middle and longwavebands. The invention provides specific values for controlling thesurface errors of the sample to ensure the precision of the homogeneitymeasurement for the optical materials under infrared short, middle andlong wavebands.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically shows a wavefront distortion caused by surfaceerrors of a sample in an infrared optical material.

FIG. 2 shows a comparison of a wavelength of infrared radiation withwhich homogeneity of infrared optical samples is measured and awavelength of visible light with which the surface error of the infraredoptical samples is inspected and evaluated.

DETAILED DESCRIPTION OF EMBODIMENTS

This invention will be further described below in detail with referenceto the accompanying drawings and embodiments to make the purpose,content and advantages of the invention clearer.

The invention sets an equation to calculate a wavefront distortion of atest light beam caused by surface errors of a sample of infrared opticalmaterials; the wavefront distortion caused by the surface errors is madeto be less than or equal to a product of a wavefront distortion inaccordance with precision requirements of a refractive index homogeneitymeasurement performed by interferometers and a precision control factor(≤1). The measurement precision requirements in infrared wavebandscorresponding to controlling the surface errors of the sample measuredwith infrared radiation is converted to the surface errors of the samplewhich is inspected with visible light. A numerical table is establishedto control the surface errors of the sample which is processed andinspected with the visible light, where various wavebands (such asshort, middle and long wavebands) used by the infrared optical materialsand interferometers which vary in principles are involved, therebyproviding algorithms and quantitative relationships to control thesurface errors of the sample in the homogeneity measurement of infraredoptical materials. The technical solution described herein offersaccurate guidance for controlling the surface errors of the sample, soas to ensure the homogeneity measurement precision of infrared opticalmaterials.

The invention provides a method for controlling the surface errors of asample in a homogeneity measurement of infrared optical materials, whichis specifically described as follows.

1) The refractive index homogeneity of the infrared optical materials isgenerally measured through an interferometry. The refractive indexinhomogeneity problems in infrared optical materials are obtained bymeasuring the wavefront distortion of reference beam waves (which areusually plane waves) which transmit through the sample. The distortionof the reference plane waves can be caused by the refractive indexinhomogeneity of infrared optical materials, as well as the surfaceerrors or surface flatness error of the infrared optical samples. Thesurface errors or flatness errors of the sample is set as S_(im), and anominal refractive index of the sample is set as n₀, and the number oftimes with which an infrared radiation flux transmits through the sampleis set as N, and two surfaces of the sample are assumed to have the sameor approximately the same surface errors. The wavefront distortion ofthe reference light waves caused by the surface errors of the sample isset as ΔW_(S), which is calculated according to equation (1):

ΔW _(S)=2N(n ₀−1)S _(im)  (1).

Even if the infrared optical sample has desired refractive indexhomogeneity, the surface errors of the sample will cause a significantemergent wavefront distortion after the incident plane waves transmitthrough the sample, as shown in FIG. 1. Such significant emergentwavefront deformation is attributed to two factors. The first factor issurface errors superposition of two surfaces of the sample. The secondfactor is that the superposition of the surface errors of the sample isamplified by the high refractive index of the infrared materials.

(2) In order to ensure the homogeneity measurement precision of infraredoptical materials, the wavefront distortion ΔW_(S) of the referencewaves caused by the surface errors S_(im) of the sample is required tobe less than or equal to a product of a wave error ΔW_(p) and aprecision control factor k, where the wave error ΔW_(p) is in accordancewith permissible precision requirements of the refractive indexhomogeneity measurement interferometers, and k may be 1, ½ or ⅓. Thesmaller the value of k, the smaller an influence of the surface errorson the measurement precision. FIG. 2 shows the relationship between thewavefront distortion ΔW_(S) and the wave error ΔW_(p), which areexpressed as inequation (2):

ΔW _(S) ≤kΔW _(P)  (2).

The equation (1) is plugged into the inequation (2) to obtain inequation(3):

$\begin{matrix}{{S_{im} \leq {k\frac{\Delta W_{p}}{2{N\left( {n_{0} - 1} \right)}}}}.} & (3)\end{matrix}$

(3) The number N is determined according to the principles of theinterferometer used for measurement. The infrared radiation fluxtransmits through the sample twice (N=2) when a Fizeau interferometer isused to measure refractive index homogeneity; the infrared radiationflux transmits through the sample twice (N=2) when a Twyman-Greeninterferometer is used to measure refractive index homogeneity; and theinfrared radiation flux transmits through the sample once (N=1) when aMach-Zehnder interferometer is used to measure refractive indexhomogeneity.

(4) Permissible precision of the interferometer is determined. Whenanyone among the Fizeau interferometer, the Twyman-Green interferometerand the Mach-Zehnder interferometer is used in the homogeneitymeasurement of the infrared optical material, the wavefront error ΔW_(p)in accordance with measurement precision requirements of theinterferometers is usually one-fifth of an infrared wavelength λ_(i) formeasurement, and thus ΔW_(p) is calculated according to equation (4):

$\begin{matrix}{{{\Delta W_{p}} = \frac{\lambda_{i}}{5}}.} & (4)\end{matrix}$

The equation (4) is plugged into the inequation (3) to obtain inequation(5):

$\begin{matrix}{{S_{im} \leq {k\frac{\lambda_{i}}{10{N\left( {n_{0} - 1} \right)}}}}.} & (5)\end{matrix}$

(5) Although the homogeneity of infrared optical materials is measuredwith an infrared light source using an infrared interferometer, theinfrared optical sample is processed and inspected with visible light.Therefore, the surface errors of the sample measured with the infraredwavelength should be converted to the surface errors of the samplemeasured with visible light wavelength, so as to accord with the actualprocessing and inspection situation of the infrared sample. The visiblewavelength for inspecting an infrared optical sample is set as λ_(v). Aratio of the infrared wavelength λ_(i) used in measuring the infraredsample to the visible wavelength λ_(v) is set as R which is expressed asequation (6):

$\begin{matrix}{{R = \frac{\lambda_{i}}{\lambda_{v}}}.} & (6)\end{matrix}$

(6) The equation (6) is plugged into the inequation (5) to obtaininequation (7), so that the surface errors of the sample of infraredoptical materials are measured by the wavelength of the visible light,where the inequation (7) is expressed as:

$\begin{matrix}{{S_{im} \leq {k\frac{R\lambda_{v}}{10{N\left( {n_{0} - 1} \right)}}}}.} & (7)\end{matrix}$

(7) Since the visible wavelength λ_(v) is 0.6328 μm, and infraredwavebands are classified into a short infrared waveband with a meanwavelength λ_(s) of 2 μm, a middle infrared waveband with a meanwavelength λ_(m) of 4 μm and a long infrared waveband with a meanwavelength λ₁ of 10 μm. λ_(s) is divided by λ_(v) to obtain a ratioR_(s) of approximately 3.16:1; λ_(m) is divided by λ_(v) to obtain aratio R_(m) of approximately 6.32:1; and λ₁ is divided by λ_(v) toobtain a ratio R₁ of approximately 15.8:1.

(8) The ratios R_(s), R_(m) and R₁ of various infrared wavebands arerespectively plugged into the inequation (7) to establish a numericaltable for controlling the surface errors of the sample corresponding tothe precision requirements of the homogeneity measurement of infraredoptical materials, as shown in Table 1, thereby establishing arelationship between control values of the surface errors of the sampleand the various precision requirements of homogeneity measurementapplications of various infrared wavebands and interferometers whichvary in principles. The surface errors of the sample for homogeneitymeasurement should be selected by equal to or less than the values shownin Table 1. Referring to Table 1, there are two measurement principleswhen N=2. One measurement principle is that a sample shape for measuringis a plane parallel plate sample, and the other measurement principle isthat the sample shape for measuring is a wedge-shaped sample. Thesurface errors of the two surface sides of the sample cannot be mutuallysubtracted when the measurement principle for the plane parallel platesample is used, and the surface errors of the two surface sides of thesample can be partly mutually subtracted when the measurement principlefor the wedge-shaped sample is used. Thus, requirements for the surfaceerrors of the sample can be lowered when the measurement principle forthe wedge-shaped sample is used.

TABLE 1 Numerical table for controlling the surface errors of the samplecorresponding to the precision requirements of the homogeneitymeasurements for infrared optical materials Number of times the infraredradiation flux Permissible surface errors in visible waveband transmitsthrough the Short infrared Middle infrared Long infrared sample wavebandwaveband waveband N = 1 $k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.58\lambda_{v}}{n_{0} - 1}$ N = 2 (without consideration ofsurface error mutual $k\frac{0.158\lambda_{v}}{n_{0} - 1}$$k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.79\lambda_{v}}{n_{0} - 1}$ offsetting) N = 2 (with surfaceerror mutual offsetting) $k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.264\lambda_{v}}{n_{0} - 1}$$k\frac{3.16\lambda_{v}}{n_{0} - 1}$

(9) A typical value of the precision control factor k is 1, and thenominal refractive index n_(o) of the chalcogenide infrared opticalmaterials which are used frequently is 2.6. k=1 and n₀=2.6 are pluggedinto Table 1 in step (8) to obtain a commonly used case table, as shownin Table 2.

TABLE 2 Case table for controlling the surface errors of the samplecorresponding to the precision requirements of the homogeneitymeasurement for the infrared optical materials Number of times theinfrared radiation flux Permissible surface errors in visible wavebandtransmits through the Short infrared Middle infrared Long infraredsample waveband waveband waveband N = 1 λ_(v)/5 2λ_(v)/5 λ_(v) N = 2λ_(v)/10 λ_(v)/5 λ_(v)/2 (without consideration of surface error mutualoffsetting) N = 2 2λ_(v)/5 4λ_(v)/5 2λ_(v) (with surface error mutualoffsetting)

(10) The surface errors of the sample in the homogeneity measurement ofthe infrared optical materials can be controlled based on the precisionrequirements of the homogeneity measurement for the infrared opticalmaterials and the surface errors of the sample shown in Table 1; thesurface errors of the sample in the homogeneity measurement of theinfrared optical materials of which refractive indexes are the same orclose to that of the infrared chalcogenide optical material can becontrolled based on the precision requirements of the homogeneitymeasurements of the infrared optical materials and the permissiblesurface errors of the sample shown in Table 2.

It can be seen that in this application, a calculation relationshipamong the surface errors of the sample in the homogeneity measurement ofthe infrared optical materials, the measurement principles and theprecision requirements is established. The wavefront distortion causedby the surface errors of the sample measured with infrared radiationshould be converted to the surface errors of the sample which isprocessed and inspected with the visible light. Through establishingrelated algorithms and formulas for numerical calculations, a numericaltable for controlling the surface errors of the sample is created toensure the precision of the homogeneity measurement for the infraredoptical materials under short, middle and long wavebands. Thecalculation is further performed to establish the case table forcontrolling the surface errors of the sample to ensure the precision ofthe homogeneity measurement for the infrared optical materials undershort, middle and long wavebands. The invention provides specific valuesof the surface errors of the sample to ensure the precision of thehomogeneity measurement for the optical materials under short, middleand long wavebands. Moreover, the technical ideas and algorithms of theapplication can also be applied to control the surface errors of thesamples for the homogeneity measurement of optical materials in visiblelight, ultraviolet light wavebands, etc., in the same way.

The invention aims to eliminate the effect of surface errors of samplesof various infrared optical materials, such as infrared optical crystal,infrared glass and infrared ceramic, on the precision of the refractiveindex homogeneity measurement, so as to allow the measurement results ofthe homogeneity measurement for the infrared optical materials toreflect real situations of the materials. Through the algorithms shownin Table 1, lot of case tables for controlling the surface errors of thesample of the homogeneity measurement for infrared optical materials canbe obtained based on refractive indexes of various infrared opticalmaterials and various precision requirements control factor values,thereby facilitating controlling the surface errors of the samples ofthe various infrared optical materials.

The above are merely exemplary embodiments of the invention. It shouldbe noted that, any improvements and modifications made by those skilledin the art without departing from the technical principles of theinvention shall fall within the scope of the invention.

What is claimed is:
 1. A method for controlling surface errors of asample in homogeneity measurements of infrared optical materials,comprising: 1) setting the surface error of the sample as S_(im), anominal refractive index of the sample as n₀, the number of times withwhich an infrared radiation flux transmits through a surface of thesample as N and a wavefront distortion of reference beam waves caused bythe surface errors of the sample as ΔW_(S); and calculating ΔW_(S)according to equation (1):ΔW _(S)=2N(n ₀−1)S _(im)  (1); 2) establishing a relationship betweenthe wavefront distortion ΔW_(S) and a wave error ΔW_(p) of permissibleprecision requirements of an interferometer for refractive indexhomogeneity measurements:ΔW _(S) ≤kΔW _(P)  (2); wherein k is the precision control factor;plugging the equation (1) into the inequation (2) to obtain inequation(3): $\begin{matrix}{{S_{im} \leq {k\frac{\Delta W_{p}}{2{N\left( {n_{0} - 1} \right)}}}};} & (3)\end{matrix}$ 3) determining the number N according to measurementprinciples of the interferometer; 4) obtaining the wave error ΔW_(p) ofthe permissible precision requirements of the interferometer accordingto permissible precision of the interferometer, and calculating the waveerror ΔW_(p) according to equation (4): $\begin{matrix}{{{\Delta W_{p}} = \frac{\lambda_{i}}{5}};} & (4)\end{matrix}$ wherein λ_(i) is the infrared wavelength for measurement;plugging the equation (4) into the inequation (3) to obtain inequation(5): $\begin{matrix}{{S_{im} \leq {k\frac{\lambda_{i}}{10{N\left( {n_{0} - 1} \right)}}}};} & (5)\end{matrix}$ 5) setting a visible wavelength for inspecting an infraredoptical sample as λ_(v), and setting a ratio of the infrared wavelengthλ_(i) to the visible wavelength λ_(v) as R; wherein R is expressed asequation (6): $\begin{matrix}{{R = \frac{\lambda_{i}}{\lambda_{v}}};} & (6)\end{matrix}$ 6) plugging the equation (6) into the inequation (5) toobtain inequation (7), so that the surface errors of the sample aremeasured with the visible wavelength, wherein the inequation (7) isexpressed as: $\begin{matrix}{{S_{im} \leq {k\frac{R\lambda_{v}}{10{N\left( {n_{0} - 1} \right)}}}};} & (7)\end{matrix}$ 7) since the visible wavelength λ_(v) is 0.6328 μm, andinfrared wavebands are classified into a short infrared waveband with amean wavelength λ_(s) of 2 μm, a middle infrared waveband with a meanwavelength λ_(m) of 4 μm and a long infrared waveband with a meanwavelength λ_(i) of 10 μm, dividing λ_(s) by λ_(v) to obtain a ratioR_(s) of approximately 3.16:1; dividing λ_(m) by λ_(v) to obtain a ratioR_(m) of approximately 6.32:1; and dividing λ_(i) by λ_(v) to obtain aratio R₁ of approximately 15.8:1; 8) plugging the ratios R_(s), R_(m)and R₁ obtained in step (7) into the inequation (7) to establish anumerical table for controlling of the surface errors of the samplecorresponding to precision requirements of the homogeneity measurementsfor the infrared optical materials, thereby establishing a relationshipbetween control values of the surface errors of the sample and variousprecision requirements for measurement applications of various infraredwavebands and interferometers which vary in principles; and 9)controlling the surface errors of the sample in the homogeneitymeasurements of the infrared optical materials based on the precisionrequirements of the homogeneity measurements of the infrared opticalmaterials and the surface errors shown in the numerical table.
 2. Themethod of claim 1, wherein k is 1, ½ or ⅓, and the smaller a value of k,the smaller an influence of the surface errors of the sample on themeasurement precision.
 3. The method of claim 1, wherein in step 3), theinfrared radiation flux transmits through the sample twice (N=2) when aFizeau interferometer is used to measure refractive index homogeneity;the infrared radiation flux transmits through the sample twice (N=2)when a Twyman-Green interferometer is used to measure the refractiveindex homogeneity; and the infrared radiation flux transmits through thesample once (N=1) when a Mach-Zehnder interferometer is used to measurethe refractive index homogeneity.
 4. The method of claim 1, wherein thenumerical table established in step 8) is shown in Table 1: TABLE 1Numerical table for controlling the surface errors of the samplecorresponding to the precision requirements of the homogeneitymeasurements for infrared optical materials Number of times the infraredradiation flux Permissible surface errors in visible waveband transmitsthrough the Short infrared Middle infrared Long infrared sample wavebandwaveband waveband N = 1 $k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.58\lambda_{v}}{n_{0} - 1}$ N = 2 (without consideration ofsurface error mutual $k\frac{0.158\lambda_{v}}{n_{0} - 1}$$k\frac{0.316\lambda_{v}}{n_{0} - 1}$$k\frac{0.79\lambda_{v}}{n_{0} - 1}$ offsetting) N = 2 (with surfaceerror mutual offsetting) $k\frac{0.632\lambda_{v}}{n_{0} - 1}$$k\frac{1.264\lambda_{v}}{n_{0} - 1}$$k\frac{3.16\lambda_{v}}{n_{0} - 1}$


5. The method of claim 4, wherein the surface errors of the sample forthe homogeneity measurements are equal to or less than the values shownin Table
 1. 6. The method of claim 4, wherein in Table 1, there are twomeasurement principles when N=2; one measurement principle is that asample shape for measuring is a plane parallel plate sample, and theother measurement principle is that the sample shape for measuring is awedge-shaped sample; and requirements of the surface errors of thewedge-shaped sample are lowered, since the surface errors of the sampleare mutually subtracted by a measurement principle of the wedge-shapedsample.
 7. The method of claim 4, wherein before the step 9), the methodfurther comprises: plugging the precision control factor k of 1 and anominal refractive index n₀ of an infrared chalcogenide optical materialof 2.6 to obtain a case table 2: TABLE 2 Case table for controlling thesurface errors of the sample corresponding to the precision requirementsof the homogeneity measurements for infrared optical materials Number oftimes the infrared radiation flux Permissible surface errors in visiblewaveband transmits through the Short infrared Middle infrared Longinfrared sample waveband waveband waveband N = 1 λ_(v)/5 2λ_(v)/5 λ_(v)N = 2 λ_(v)/10 λ_(v)/5 λ_(v)/2 (without consideration of surface errormutual offsetting) N = 2 2λ_(v)/5 4λ_(v)/5 2λ_(v) (with surface errormutual offsetting)


8. The method of claim 4, wherein the surface errors of the sample inthe homogeneity measurements of various infrared optical materials arecontrolled based on the precision requirements of the homogeneitymeasurements for the infrared optical materials and the surface errorsof the sample shown in Table 1; the surface errors of the sample in thehomogeneity measurements of the infrared optical materials withrefractive indexes the same or close to that of the infraredchalcogenide optical material are controlled based on the precisionrequirements of the homogeneity measurements of the infrared opticalmaterials and the permissible surface errors of the sample shown inTable
 2. 9. The method of claim 7, wherein the surface errors of thesample in the homogeneity measurements of various infrared opticalmaterials are controlled based on the precision requirements of thehomogeneity measurements for the infrared optical materials and thesurface errors of the sample shown in Table 1; the surface errors of thesample in the homogeneity measurements of the infrared optical materialswith refractive indexes the same or close to that of the infraredchalcogenide optical material are controlled based on the precisionrequirements of the homogeneity measurements of the infrared opticalmaterials and the permissible surface errors of the sample shown inTable 2.